Absolute Value Inequalities

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What does the inequality |x| < a represent?

Back

It represents the values of x that are within a distance a from 0 on the number line.

Front

What does the inequality |x| > a represent?

Back

It represents the values of x that are more than a distance a from 0 on the number line.

Front

Solve: |p + 3| ≥ 10

Back

p ≤ -13 or p ≥ 7

Front

Solve: 3 | 2x + 7| - 7 < -4

Back

x < -3 and x > -4

Front

Solve: 6 - 2|m - 3| > -4

Back

-2 < m < 8

Front

Solve: |x + 3| > -8

Back

all real numbers

Front

What is the solution set for |x| < 5?

Back

-5 < x < 5

Front

What is the solution set for |x| > 2?

Back

x < -2 or x > 2

Front

How do you solve an absolute value inequality?

Back

1. Isolate the absolute value expression. 2. Set up two separate inequalities based on the definition of absolute value. 3. Solve each inequality.